Magnetohydrodynamics free convection flow of incompressible fluids over corrugated vibrating bottom surface with Hall currents and heat and mass transfers considering heat flux is discussed. The corrugation patterns suggested are sinusoidal in nature. The governing equations are solved by the explicit finite difference numerical method of the forward-time backward-space scheme to obtain the analytical results for velocity, concentration, and temperature profiles. The unsteady resultant velocities, concentration, and temperature for various values of physical parameters are discussed in detail, and it is shown that they have significant effects on the fluid flow, and heat and mass transfers are shown graphically.

The formation of solid wax crystals, which interlock and form a gel-like layer on the inner wall of the crude oil pipeline, influences the transportation of waxy crude oil. The deposited layer grows continuously and hardens during the oil transportation, reducing the effective inside diameter of the crude oil pipeline and the flow rate. In extreme cases, the deposited layer may block the crude oil pipeline leading to a loss of production and capital investment. In this paper, wax deposition from multiphase flow in field-scale oil pipeline transport systems has been studied. The novelty of this work is to develop a mathematical model that incorporates water-in-oil emulsions, wax precipitation kinetics, molecular diffusion, and shear dispersion to enable accurate predictions of both the wax deposit growth rate and aging of the deposit. The coupled nonlinear partial differential equations governing the flow are discretized in time by a second-order semi-implicit time discretization scheme based on the Adams-Bashforth and Crank-Nicolson methods, which completely decouples the computation of the governing equations. The resulting temporal schemes are discretized in space by the bivariate spectral collocation method based on Chebyshev-Gauss-Lobatto grid points and simulated in MATLAB software to obtain the profiles of the flow variables. The simulation results are presented in graphical and in tabular forms and discussed. This study found that the deposit thickness is directly proportional to the Reynolds number and inversely proportional to the mass Grashof number, Schmidt number, and Weber number. Deposit aging is rampant during the early stages of wax deposition, after which it stabilizes at a specific value as time elapses. A deposition model to predict the wax deposit thickness and aging is proposed in this study. The findings of this study will help in making informed decisions on the planning of pigging operations, thermal insulation, and other remediation techniques to be applied in controlling wax deposition in field-scale crude oil pipeline systems.

Analysis of magnetohydrodynamics flow of incompressible fluids over an oscillating bottom surface with heat and mass transfer is discussed. The flow is free convection in nature. Momentum, energy, and concentration equations are obtained for computation of their respective profiles. The unsteady flow two-dimensional governing equations are solved numerically by the explicit finite difference method of the Forward Time Backward Space scheme. The numerical results show that the applied parameters have significant effects on the fluid flow and heat transfer and have been discussed with the help of graphical illustrations.

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